Deck of cards and 17-gons
Source: Schweitzer 2009
November 13, 2009
symmetrygraph theorycombinatorics proposedcombinatorics
Problem Statement
On every card of a deck of cards a regular 17-gon is displayed with all sides and diagonals, and the vertices are numbered from 1 through 17. On every card all edges (sides and diagonals) are colored with a color 1,2,...,105 such that the following property holds: for every 15 vertices of the 17-gon the 105 edges connecting these vertices are colored with different colors on at least one of the cards. What is the minimum number of cards in the deck?